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On negative compounds: a parallel between Pāṇini and Aristotle


– Sergiu Al-George (1922-1981) –

Like many other aspects of his work, Pāṇini’s treatment of negative compounds is not relevant only to linguistics, but to logic as well. The complex significance of negative compounds arose in both Indian and Western culture as a problem of interdisciplinary interest: expressions like “non-man”, “non-brahman” or “non-being” were thus equally taken into consideration by grammarians, logicians and metaphysicians. The fact that Pāṇini offered an interpretation of negative compounds before they received a treatment in Indian texts of logic has gone unnoticed not only in studies dealing with Indian philosophy in general, but even in those dealing with the specific problem of negation.

The logical relevance of the Pāṇinian approach to negative compounds is brought out by a comparison with Aristotle. This comparison comes naturally, as in both cases identical linguistic structures are analysed, which belong to the same Indo-European family. Moreover, the respective analyses were performed approximately at the same time by two great thinkers who played a prominent and, somewhat, analogous part in the development of their own cultures.

In De Interpretatione, in the chapter dealing with “The Simple noun and the nominal compound” (2, 16a), after a very summary distinction between the respective types of nouns, based on the idea that the nominal compound is more determinate than the simple noun, Aristotle contends that a negative compound like “non-man” is not a noun; the reason he provides for this thesis is that there is no corresponding definite reference for such an expression, which he consequently calls “indeterminate noun”. In the same book (10, 20a), this time in connection with simple judgments, where the subject is either determinate or indeterminate, the Stagirite provides further arguments in support of his thesis. He considers that by employing the expression “non-man” one is not nearer to, but farther from making a true or untrue statement than by employing the expression “man”.

Like Aristotle, Pāṇini discusses negative compounds under the general category of nominal compounds, but the latter are treated in more detail in the Astadhyayi. Here, instead of the general and self-evident statement that nominal compounds are more determinate than simple nouns, we find a subtle and rigorous typology encroaching on the territory of logic.

Pata4jali (on II, 1, 6) observed that under Pāṇini’s four types of nominal compounds (samasa), i. e. avyayibhava, tatpurusa, bahuvrihi and dvanvda, there lies a fourfold grouping of two qualities, the principal (pradhana) and the secondary (apradhana upasarjana) which, in the binary relationship of logical determination, become determinandum and determinans respectively. If, as B. Liebich[1] suggested, we represent the pradhana by “+” and the apradhana by “–”, there are only four possible groupings: + –, – +, – –, + +. These four groupings correspond respectively to the four types in the Pāṇinian classification. The first two types, avyayibhava and tatpurusa, are symmetrical inasmuch as their constituents are in contrast, thus representing an instance of internal determination between the principal and the secondary; on the other hand, in bahuvrihi and dvandva there is no contrast between the two constituents and the compound in its totality is related to some other word of the sentence.

A reference to the samasa classification was necessary not only in order to appreciate its logical insight, but also to gain a better understanding of the negative compounds’ structure, in relation to the respective classification. According to Pāṇini (II, 2, 6), negative compounds, called na4-samasa, belong to the tatpurusa class and consequently the negative particle that represents the secondary constituent becomes the determinans of the noun. More specifically, the negative particle belongs to the subclass of descriptive determinatives (karmadharaya), and its function is that of an appositional attribute in relation to a noun. This determinative function is also explicitely stated by Pāṇini in s2tra II, 1, 60, where he speaks of the negated noun as na4-viśista, “qualified by na4”. As Patańjali observes (on II, 2, 6), the negative particle is a viśesaka, “qualifier”, and is therefore assigned a definite logical interpretation. In contradistinction to Aristotle, the negative compound is no less determinate than any other compound of its class.

Upon a closer examination, this contrast in treatment would indicate a difference in the way the extension of a negative compound was conceived by the two thinkers. As Pata4jali explained, the employment of the negative particle suppresses the meaning of the negated noun[2], and thus, in logical terms, it has only an extensive value. But the extension, in this case, seems susceptible of a twofold interpretation: it either includes the whole universe – except the reference of the noun under negation – and as such is practically infinite, or it is confined to a definite field. The former interpretation was obviously favoured by Aristotle, whereas the latter by Pāṇini.

It is hard to find in Aristotle a clear illustration in support of his own interpretation. In his judgment theory, the negative expression “non-A” is considered either as a possible subject or as an attributive predicate. However, in his treatment of contradiction and contrariety relationships (Analitica Priora I, 46, 51b‑52a), he lays particular emphasis on negative predicates in order to distinguish between the assertion of an indeterminate attribute (“is non‑A”) and the negation of a determinate one (“is not A”). On the contrary, Pāṇini’s work provides a comprehensive illustration of his interpretation: negative compounds are freely employed regardless of their being ambiguous or indefinite as to their extension. According to the exegetical literature, there is ambiguity only as to whether the privative nañ in some compounds should be understood as belonging with the noun following it (paryudasa) or with a verbal idea (prasajyapratisedha); thus, there is ambiguity only as to whether a negative particle joined to a noun is really a nañsamasa or not.

One would be tempted to explain the contrast between the Pāṇinian and the Aristotelian treatment by saying that the grammarian’s mental universe, being restricted to a finite metalanguage, is more limited than the logician’s, but the real explanation is more profound. For instance, the technical term ati7, which is the negated form of ti7, “verb personal endings”, should not be taken to denote the remainder of the technical vocabulary; it denotes only the primary suffixes (krt) which, like ti7, are added to the verbal root (dhatu). Thus, in Pāṇini’s thinking, it is clear that the extension of a negative compound is restricted to the field of similar terms. This major principle is clearly stated in paribhasa 74:

[The word] to which na4 or iva are attached [denotes] a locus which is distinct but similar [to that the of negated word], for thus is the meaning [according to the ordinary use][3].

Patañjali illustrates the ordinary use by means of the same example, abrahmana, “non‑brahman”, which illustrates the nañsamasa (on II, 2, 6). This negative compound does not denote just any individual, but someone who belongs to the caste system. Thus, Pāṇini’s theory and use of negative compounds are in accordance with the object language. Therefore, negative particles are not considered unilaterally, in their oppositive function (contrariety or contradiction), but more comprehensively, in a dialectics where otherness and likeness have equal weight.

A parallel to Pāṇini’s treatment was developed in Europe only much later, in the nineteenth century. Until then, the Aristotelian view had prevailed. In the Middle Ages every negation was considered to be indefinite (“omnis negatio vero indefinita est”) and, even in the eighteenth century, Kant qualified a judgment containing negative predicative attribute as an “infinite judgment”. Only later did mathematical logic produce a different interpretation, by using the calculus of classes and set theory: “non-A” or “A” is contextually limited by the “universe of discourse” which is a finite basic set. Accordingly, “non-A” or “A” is defined as the difference between this basic set “U” and the set designated by the negated term “A”: A = U – A. If “U” stands for the class of vertebrates and “A” for that of viviparous animals, then “A” represents the class of non-viviparous vertebrates. “A” and “A” are complementary classes; the extension of a term under negation is its complementary class.

To say that a negative particle operates in the field of complementarity is only a different and, of course, a less explicit way of expressing the dialectical properties of the negative particle which functions in a locus coincidentally different and similar. After almost twenty-five centuries, European logicians attempted to revise Aristotle’s analysis and came up, in fact, with Pāṇini’s own analysis.

The logical purport of Pāṇini’s analysis of nominal compounds can be better appreciated if we observe that negation holds a crucial place in the science of reasoning; this logical purport can futhermore be illustrated by reference to the Indian philosophical tradition. Should such a study be undertaken, it would reveal that Pāṇini’s treatment of negative particles laid the groundwork for later logical‑semantic developments. The famous buddhist apoha theory, according to which the meaning of a word is established by “the exclusion of its otherness” (anyapoha), is a case in point: the meaning of the word “cow” is the exclusion of “non-cow”. The “otherness” (anya) of a word – expressed by joining it to the privative particle to form a compound – is to be understood as determinate itself, or else its exclusion would be deprived of determination. Another instance is provided by Navya-Nyaya where negative cognition is regarded – along the line laid down by Pāṇini – as viśistajñana, “determinate cognition”. But all these topics, which lie in fact beyond the scope of the present paper, will be discussed elsewhere.

[1] B. Liebich, Zwei Kapitel der Kaçika, Breslau 1892, p. VII.

[2]MBh ad II, 2, 6: nañ-prayujyamanah padartham nivartayati (p. 411, ll. 5-6).

[3]MBh ad III, 1, 12, after varttika 4: nañivayuktam anyasadadhikarane tatha hy arthagatih/